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arXiv · 2509.08121

An Algorithmic Upper Bound for Permanents via a Permanental Schur Inequality

Aditi Laddha·Madhusudhan Reddy Pittu
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Abstract

Computing the permanent of a non-negative matrix is a computationally challenging, \#P-complete problem with wide-ranging applications. We introduce a novel permanental analogue of Schur's determinant formula, leveraging a newly defined \emph{permanental inverse}. Building on this, we introduce an iterative, deterministic procedure called the \emph{permanent process}, analogous to Gaussian elimination, which yields constructive and algorithmically computable upper bounds on the permanent. Our framework provides particularly strong guarantees for matrices exhibiting approximate diagonal dominance-like properties, thereby offering new theoretical and computational tools for analyzing and bounding permanents.

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Aditi Laddha, Madhusudhan Reddy Pittu. 2025-09-09. An Algorithmic Upper Bound for Permanents via a Permanental Schur Inequality. https://arxiv.org/abs/2509.08121

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